Advanced Matrix Analysis
- Garant předmětu:
- Department of Mathematics
This is a continuation of linear algebra. A relatively good knowledge of basic notions of linear algebra is supposed. The aim is to explain spectral theorems and their applications. Further Jordan form of a matrix and functions of a matrix are studied.
- Syllabus of lectures:
1. A recapitulation of basic notions of linear algebra.
2. Real and complex matrices, matrix algebra.
3. Eigenvalues and eigenvectors of square matrices.
4. Diagonalization of a square matrix, conditions of diagonalizability.
5. Standars inner product, orthogonalization, orthogonal projection.
6. Unitary matrices, the Fourier matrix.
7. Eigenvalues and eigenvectors of hermitian and unitary matrices.
8. Spectral theorem for hermitian matrices.
9. Definite matrices, characterization in terms of eigenvalues.
10. Least squares, algebraic formulation, normal equations.
11. Singular value decomposition, application to lest squares.
12. Jordan form of a matrix.
13. Function of a matrix, definition and computation.
14. Power series representation of a matrix function, some application.
- Syllabus of tutorials:
- Study Objective:
- Study materials:
1. C. D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM 2000
2. M. Dont: Maticová analýza, skripta, nakl. ČVUT 2011
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: